Clearing Markets via Bundles

  • Michal Feldman
  • Brendan Lucier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8768)


We study algorithms for combinatorial market design problems, where a set of heterogeneous and indivisible objects are priced and sold to potential buyers subject to equilibrium constraints. Extending the CWE notion introduced by Feldman et al. [STOC 2013], we introduce the concept of a Market-Clearing Combinatorial Walrasian Equilibium (MC-CWE) as a natural relaxation of the classical Walrasian equilibrium (WE) solution concept. The only difference between a MC-CWE and a WE is the ability for the seller to bundle the items prior to sale. This innocuous and natural bundling operation imposes a plethora of algorithmic and economic challenges and opportunities. Unlike WE, which is guaranteed to exist only for (gross) substitutes valuations, a MC-CWE always exists. The main algorithmic challenge, therefore, is to design computationally efficient mechanisms that generate MC-CWE outcomes that approximately maximize social welfare. For a variety of valuation classes encompassing substitutes and complements (including super-additive, single-minded and budget-additive valuations), we design polynomial-time MC-CWE mechanisms that provide tight welfare approximation results.


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  1. 1.
    Andelman, N., Mansour, Y.: Auctions with budget constraints. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 26–38. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Arrow, K.J., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica 22, 265–290 (1954)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Azar, Y., Birnbaum, B., Karlin, A.R., Mathieu, C., Nguyen, C.T.: Improved approximation algorithms for budgeted allocations. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 186–197. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Bikhchandani, S., Mamer, J.W.: Competitive equilibrium in an exchange economy with indivisibilities. Journal of Economic Theory 74(2), 385–413 (1997)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Bikhchandani, S., Ostroy, J.M.: The package assignment model. Journal of Economic Theory 107(2), 377–406 (2002)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Chakrabarty, D., Goel, G.: On the approximability of budgeted allocations and improved lower bounds for submodular welfare maximization and gap. In: FOCS 2008 (2008)Google Scholar
  7. 7.
    Feige, U., Vondrak, J.: Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e. In: 47th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2006, pp. 667–676 (October 2006)Google Scholar
  8. 8.
    Feldman, M., Gravin, N., Lucier, B.: Combinatorial walrasian equilibrium. In: STOC, pp. 61–70 (2013)Google Scholar
  9. 9.
    Fiat, A., Wingarten, A.: Envy, multi envy, and revenue maximization. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 498–504. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Fu, H., Kleinberg, R., Lavi, R.: Conditional equilibrium outcomes via ascending price processes with applications to combinatorial auctions with item bidding. In: ACM Conference on Electronic Commerce, p. 586 (2012)Google Scholar
  11. 11.
    Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. J. of Economic Theory 87(1), 95–124 (1999)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Guruswami, V., Hartline, J.D., Karlin, A.R., Kempe, D., Kenyon, C., McSherry, F.: On profit-maximizing envy-free pricing. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2005 (2005)Google Scholar
  13. 13.
    Holzman, R., Kfir-Dahav, N., Monderer, D., Tennenholtz, M.: Bundling equilibrium in combinatorial auctions. Games and Economic Behavior 47(1), 104–123 (2004)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Kelso Jr., A.S., Crawford, V.P.: Job matching, coalition formation, and gross substitutes. Econometrica 50(6), 1483–1504 (1982)CrossRefMATHGoogle Scholar
  15. 15.
    Mirrokni, V., Schapira, M., Vondrak, J.: Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions. In: Proceedings of the 9th ACM Conference on Electronic Commerce, EC 2008, pp. 70–77. ACM, New York (2008)Google Scholar
  16. 16.
    Nisan, N., Segal, I.: The communication requirements of efficient allocations and supporting prices. Journal of Economic Theory 129(1), 192–224 (2006)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Shapley, L.S., Shubik, M.: The assignment game i: The core. International Journal of Game Theory 1, 111–130 (1971), doi:10.1007/BF01753437CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Srinivasan, A.: Budgeted allocations in the full-information setting. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 247–253. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Michal Feldman
    • 1
  • Brendan Lucier
    • 2
  1. 1.Tel Aviv University and Microsoft ResearchTel AvivIsrael
  2. 2.Microsoft ResearchCambridgeUSA

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